Abstarct: The purpose of this study is free vibration and buckling analysis of functionally graded cylindrical shell, subjected to static axial load. Material properties of functionally graded cylindrical shell are considered as temperature dependent and graded in the thickness direction according to a power-law distribution. The study is baxsed on third-order shear deformation theory and the obtain equations is conducted on the principle of Hamilton. After obtaining the equations of motion using strain-displacement relations baxsed on first approximation love and replacing them in stress-strain relations, eventually equations of motion is written in terms of displacement components. Boundary conditions of the shell are considered simply supported at both ends. Taking into account the boundary conditions of shell, a displacement field which satisfies the boundary conditions for solving the equations of motion is assumed. Finally, buckling load and natural frequencies are extracted and effects of changes in geometry parameters, material properties, and axial load on buckling load and natural frequency on the structure were discussed. By comparing the results with the references, accuracy of solutions has been validated as well as the increased precision of third-order shear deformation theory.